source("utils.R")Compute UVP diversity metrics
Compute taxonomic, morphologic and trophic diversity metrics from UVP5 plankton data.
Read UVP data
load("data/02.all_uvp.Rdata")Clean data
Depth
Keep only organisms above the depth at which we want to predict poc export, i.e. 1000 m.
o <- o %>% filter(depth < max_depth_uvp)Taxa
List taxa, merge contextual observations with regular observations. Remove some unwanted taxa: tentacles of Cnidaria (only part of organisms, not representative of the overall morphology), Trichodesmium, Nostocales and Bacillariophyta (phytoplankton).
# List of taxa
taxa <- o %>% pull(taxon) %>% unique() %>% sort()
taxa [1] "Acantharea" "Actinopterygii"
[3] "Annelida" "Appendicularia"
[5] "Bacillariophyta (contextual)" "Cephalopoda"
[7] "Chaetognatha" "colonial Collodaria"
[9] "Copepoda" "Ctenophora"
[11] "Doliolida" "Eumalacostraca"
[13] "Foraminifera" "Gymnosomata"
[15] "Limacinidae" "Narcomedusae"
[17] "Nostocales" "Ostracoda"
[19] "other Cnidaria" "other Collodaria"
[21] "other Crustacea" "other Hydrozoa"
[23] "other Mollusca" "other Rhizaria"
[25] "Phaeodaria" "Pyrosoma"
[27] "Salpida" "Siphonophorae"
[29] "tentacle of Cnidaria" "Thecosomata"
[31] "Trachymedusae" "Trichodesmium"
[33] "Trichodesmium (contextual)" # Merge contextual
o <- o %>% mutate(taxon = str_remove_all(taxon, " \\(contextual\\)")) # NB need to use \\
# List unwanted taxa
unwanted <- c("Bacillariophyta", "Nostocales", "tentacle of Cnidaria", "Trichodesmium")
o <- o %>% filter(!taxon %in% unwanted)
# New list of taxa
taxa <- o %>% pull(taxon) %>% unique() %>% sort()
taxa [1] "Acantharea" "Actinopterygii" "Annelida"
[4] "Appendicularia" "Cephalopoda" "Chaetognatha"
[7] "colonial Collodaria" "Copepoda" "Ctenophora"
[10] "Doliolida" "Eumalacostraca" "Foraminifera"
[13] "Gymnosomata" "Limacinidae" "Narcomedusae"
[16] "Ostracoda" "other Cnidaria" "other Collodaria"
[19] "other Crustacea" "other Hydrozoa" "other Mollusca"
[22] "other Rhizaria" "Phaeodaria" "Pyrosoma"
[25] "Salpida" "Siphonophorae" "Thecosomata"
[28] "Trachymedusae" Profiles
Compute the number of objects per profile and keep only profiles that have more than 10 objects.
profiles <- o %>%
group_by(profile_id, lon, lat, datetime) %>%
summarise(n_obj = n()) %>%
ungroup()
profiles %>%
ggplot() +
geom_histogram(aes(x = n_obj), bins = 50) +
scale_x_continuous(limits = c(0, 50)) #+
#scale_y_continuous(trans = "log1p")
#scale_y_log10()profiles %>%
ggplot() +
geom_polygon(data = world, aes(x = lon, y = lat, group = group), fill = "gray") +
geom_point(aes(x = lon, y = lat, colour = n_obj > n_min_uvp), size = 0.5) +
scale_x_continuous(expand = c(0, 0)) + scale_y_continuous(expand = c(0, 0)) +
coord_quickmap()
# Keep only profiles with enough objects
profiles <- profiles %>% filter(n_obj > n_min_uvp) %>% select(-n_obj)
# Drop objects that do not belong to these profiles
o <- o %>% filter(profile_id %in% profiles$profile_id)We have 320927 objects belonging to 2876 profiles.
Abundance and biovolume
Compute overall abundance and biovolume for each profiles.
# For abundance, just count objects per profile
profiles <- profiles %>%
left_join(o %>% count(profile_id, name = "abund"), by = join_by(profile_id))
# For biovolume, compute biovolume for each object and sum per profile
biov <- o %>%
select(object_id:taxon, esd) %>%
mutate(biovol = (4/3) * pi * esd^3) %>%
group_by(profile_id) %>%
summarise(biovol = sum(biovol))
# add to profiles
profiles <- profiles %>% left_join(biov, by = join_by(profile_id))
## Plot maps
ggmap(profiles, var = "abund", type = "point", palette = scale_colour_viridis_c(trans = "log1p")) 
ggmap(profiles, var = "biovol", type = "point", palette = scale_colour_viridis_c(trans = "log1p")) 
Taxonomic diversity
Tabula package for diversity indices: https://cran.r-project.org/web/packages/tabula/vignettes/diversity.html
Species richness
number of species = Richness
Margalef’s
Menhinick’s
Diversity / evenness indices
Shannon
Brillouin
Simpson
# Generate a contingency table as a matrix to compute indices
cont <- o %>%
count(profile_id, taxon) %>%
pivot_wider(names_from = "taxon", values_from = "n", values_fill = 0) %>%
as.data.frame() %>%
column_to_rownames(var = "profile_id") %>%
as.matrix()
# test for profile id 100
# 65 objects
# 7 taxa
# (7-1)/log(65) # Margalef
# 7/sqrt(65) # Menhinick
# all godd
# Compute diversity metrics
ta_div_prof <- tibble(
profile_id = rownames(cont),
# Richess
ta_ric_1 = specnumber(cont), # species count
ta_ric_2 = (specnumber(cont) - 1)/log(rowSums(cont)), # Margalef
ta_ric_3 = specnumber(cont)/sqrt(rowSums(cont)), # Menhinick
# Heterogeneity/evenness
ta_div_1 = heterogeneity(cont, method = "shannon"),
ta_eve_1 = evenness(cont, method = "shannon"),
ta_div_2 = heterogeneity(cont, method = "brillouin"),
ta_eve_2 = evenness(cont, method = "brillouin"),
ta_div_3 = heterogeneity(cont, method = "simpson"),
ta_eve_3 = evenness(cont, method = "simpson"),
# Master predictor
ta_mast = specnumber(cont)/rowSums(cont)
) %>%
left_join(profiles, by = join_by(profile_id)) %>%
select(profile_id, lon, lat, contains("_"))
# Quick PCA to see correlations
ta_pca <- FactoMineR::PCA(ta_div_prof %>% select(-c(profile_id, lon, lat)), graph = FALSE)
plot(ta_pca, choix = "var")
# ta_eve_1 and ta_eve_2 are strongly correlated, ignore one
ta_div_prof <- ta_div_prof %>% select(-ta_eve_2)
# Store results with table of profiles
profiles <- profiles %>% left_join(ta_div_prof, by = join_by(profile_id, lon, lat))
# ta_eve_1 could not be computed for 9 profiles
# replace by mean value
profiles <- profiles %>% mutate_all(~ifelse(is.na(.x), mean(.x, na.rm = TRUE), .x)) Plot taxonomic diversity metrics.
ggmap(
profiles,
"ta_ric_1",
type = "point"
)
ggmap(
profiles,
"ta_div_1",
type = "point"
)
ggmap(
profiles,
"ta_eve_1",
type = "point"
)
Size spectra
Compute SS
Compute ss for each profiles.
# Compute SS
# Also compute mean ESD per profile and retain it
ss <- o %>%
arrange(profile_id) %>%
group_by(profile_id) %>%
mutate(mean_esd = mean(esd)) %>%
ungroup() %>%
group_by(profile_id, mean_esd) %>%
reframe(nbss(esd, type = "abundance", base = 10, binwidth = 0.1))
# Plot a few SS, in a log-transformed space
sam_profiles <- profiles %>% slice_sample(n = 12) %>% pull(profile_id)
ss %>%
filter(profile_id %in% sam_profiles) %>%
ggplot() +
geom_point(aes(x = bin, y = norm_y)) +
scale_x_log10() +
scale_y_log10() +
facet_wrap(~profile_id)
Clean SS
We need to remove the part left of the peak and keep only profiles that have at least 5 points to fit the SS.
# Use a cumulative sum to remove the part left of the peak
ss <- ss %>%
group_by(profile_id, mean_esd) %>%
# Cut the left part of the SS
filter(cumsum(norm_y == max(norm_y)) > 0) %>%
ungroup()
# Keep only profiles with at least 5 points to fit SS
ss <- ss %>% add_count(profile_id) %>% filter(n >= 5)Fit SS
## Fit size spectra
# Log-transform the y value
# NB: not necessary to log-transform x value because already present in the data
ss <- ss %>% mutate(norm_y = log10(norm_y))
# Fit lm
ss_regs <- ss %>%
select(profile_id, bin_log, norm_y) %>%
nest(data = c(bin_log, norm_y)) %>%
mutate(
fit = map(data, ~lm(norm_y ~ bin_log, data = .x)), # run lm's
glance = map(fit, glance), # summary of fit
tidied = map(fit, tidy) # extract coefficients
)
# glance contains all summary of fits
ss_summ <- ss_regs %>%
select(profile_id, glance) %>%
unnest(glance)
summary(ss_summ) profile_id r.squared adj.r.squared sigma
Length:2502 Min. :0.1229 Min. :-0.1694 Min. :0.02408
Class :character 1st Qu.:0.8646 1st Qu.: 0.8346 1st Qu.:0.16401
Mode :character Median :0.9243 Median : 0.9096 Median :0.21615
Mean :0.8955 Mean : 0.8728 Mean :0.22696
3rd Qu.:0.9583 3rd Qu.: 0.9501 3rd Qu.:0.27682
Max. :0.9979 Max. : 0.9974 Max. :0.77298
statistic p.value df logLik
Min. : 0.4205 Min. :0.0000000 Min. :1 Min. :-11.0120
1st Qu.: 31.5422 1st Qu.:0.0000310 1st Qu.:1 1st Qu.: 0.1849
Median : 64.9228 Median :0.0004526 Median :1 Median : 1.9727
Mean : 104.9461 Mean :0.0078424 Mean :1 Mean : 2.1286
3rd Qu.: 128.0728 3rd Qu.:0.0041306 3rd Qu.:1 3rd Qu.: 3.9785
Max. :1970.6414 Max. :0.5628978 Max. :1 Max. : 13.6746
AIC BIC deviance df.residual
Min. :-21.349 Min. :-20.801 Min. :0.001739 Min. : 3.000
1st Qu.: -1.957 1st Qu.: -2.126 1st Qu.:0.132587 1st Qu.: 4.000
Median : 2.055 Median : 1.772 Median :0.240737 Median : 5.000
Mean : 1.743 Mean : 1.659 Mean :0.331061 Mean : 5.394
3rd Qu.: 5.630 3rd Qu.: 5.446 3rd Qu.:0.420947 3rd Qu.: 6.000
Max. : 28.024 Max. : 29.218 Max. :4.769341 Max. :13.000
nobs
Min. : 5.000
1st Qu.: 6.000
Median : 7.000
Mean : 7.394
3rd Qu.: 8.000
Max. :15.000 # tidied contains coefficients
ss_coef <- ss_regs %>%
select(profile_id, tidied) %>%
unnest(tidied) %>%
# keep only estimates of slope and intercept
select(-c(std.error, statistic, p.value)) %>%
mutate(term = ifelse(term == "bin_log", "b1", "b0")) %>%
# 2 lines (intercept + slope) for each profile, reshape to make it one line
pivot_wider(names_from = term, values_from = estimate) #%>%
# b0 is intercept, b1 is slope
#select(profile_id, b1, b0)
summary(ss_coef) profile_id b0 b1
Length:2502 Min. :0.7447 Min. :-6.4252
Class :character 1st Qu.:1.3731 1st Qu.:-3.2741
Mode :character Median :1.6916 Median :-2.7109
Mean :1.7003 Mean :-2.7735
3rd Qu.:1.9752 3rd Qu.:-2.1931
Max. :3.6189 Max. :-0.4048 # Let’s join both together
ss_coef <- ss_coef %>% left_join(ss_summ, by = join_by(profile_id))
# Plot a few fits
ss %>%
filter(profile_id %in% sam_profiles) %>%
ggplot() +
geom_point(aes(x = bin_log, y = norm_y)) +
geom_abline(
data = ss_coef %>% filter(profile_id %in% sam_profiles),
aes(slope = b1, intercept = b0, colour = adj.r.squared)
) +
labs(x = "bin (log)", y = "norm_y (log)", colour = "adj R²") +
scale_colour_viridis_c() +
facet_wrap(~profile_id)
Save SS
Join ss outputs with profile data. For profiles for which SS could not be computed (not enough points), replace slope and intercept by the mean value.
profiles <- profiles %>%
# join slope and intercept data
left_join(ss_coef %>% select(profile_id, ss_slope = b1, ss_inter = b0), by = join_by(profile_id)) %>%
# replace by the mean value for missing profiles
mutate_all(~ifelse(is.na(.x), mean(.x, na.rm = TRUE), .x)) Morphological diversity
Based on:
Features
Some features are not meaningful for the morphology and thus should be removed. Other features have a unique value for all individuals and other are missing for many individuals. Let’s remove them.
# Select features
# NB this excludes ratio of features, e.g. kurt_mean which is kurt/mean
x <- o %>% select(area:circex)
# Remove variables with zero variance
feats <- x %>%
summarise_all(var, na.rm = TRUE) %>%
pivot_longer(cols = everything()) %>%
filter(value > 0) %>%
pull(name)
x <- x %>% select(all_of(feats))Plot features distributions.
x %>%
pivot_longer(cols = everything()) %>%
ggplot() +
geom_histogram(aes(x = value), bins = 50) +
facet_wrap(~name, scales = "free")
For a PCA, features should be normally-distributed. Let’s apply some transformation to get closer to normal distribution:
mask extreme values
normalize using the Yeo-Johnson transformation
replace missing values by the mean of each column
x_norm <- x %>%
# remove the most extreme high values
mutate_all(mask_extreme, percent = c(0, 0.5)) %>%
# normalise using the Yeo-Johnson transformation
mutate_all(yeo_johnson) %>%
mutate_all(as.numeric)
# Replace NA by average of each column
for (col in names(x_norm)) {
x_norm[[col]][is.na(x_norm[[col]])] <- mean(x_norm[[col]], na.rm=TRUE)
}Plot “normalized” features.
x_norm %>%
pivot_longer(cols = everything()) %>%
ggplot() +
geom_histogram(aes(x = value), bins = 50) +
facet_wrap(~name, scales = "free")
Morphospace
Build
Let’s feed the features to a PCA to build a morphospace.
# We need to use "scale.unit = TRUE" to center-scale all feature
mo_space <- FactoMineR::PCA(x_norm, scale.unit = TRUE, graph = FALSE)Eigenvalues
Plot the eigenvalues.
eig <- mo_space$eig %>%
as.data.frame() %>%
rownames_to_column(var = "comp") %>%
as_tibble() %>%
mutate(
comp = str_remove(comp, "comp "),
comp = as.numeric(comp),
comp = as.factor(comp)
) %>%
rename(var = `percentage of variance`, cum_var = `cumulative percentage of variance`)
eig %>%
ggplot() +
geom_col(aes(x = comp, y = eigenvalue)) +
geom_hline(yintercept = 1, col = "red", linewidth = 0.5) +
theme_classic() +
scale_y_continuous(expand = c(0, 0)) +
labs(x = "PC", y = "Eigenvalue") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))
Most of the variance is captured by the first three axes (0.33, 0.19 and 0.097respectively).
Let’s plot this in log to have a better idea of PCs to select.
eig %>%
ggplot() +
geom_path(aes(x = as.numeric(comp), y = eigenvalue)) +
geom_point(aes(x = as.numeric(comp), y = eigenvalue)) +
geom_vline(xintercept = 5, colour = "red") +
theme_classic() +
scale_x_log10() +
scale_y_log10() +
labs(x = "PC", y = "Eigenvalue") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))
It’s linear until ~5, let’s keep the first 5 PCs.
Features and axis definition
Let’s now plot the first two axes.
plot(mo_space, choix="var", axes = c(1, 2))
PC1: big objects in positive values, small objects in negative values.
PC2: clear (i.e. transparent) objects in positive values, dark (i.e. opaque) objects in negative values
As well as axes 3 and 4.
plot(mo_space, choix="var", axes = c(3, 4))
- PC3: elongated objects in positive values, round objects in negative values
- PC4: something with grey levels
Individuals
Let’s extract the coordinates of individuals in the morphospace.
## Get coordinates of individuals
inds <- mo_space$ind$coord %>% as_tibble()
# Set nice names for columns
colnames(inds) <- str_c("mo_dim", paste(c(1:ncol(inds))))
# And join with initial dataframe of objects
o <- o %>%
bind_cols(inds)We can not plot the position of objects in the morphospace, coloured per profile.
## Plot invidivuals with profile as colour
o %>%
ggplot(aes(x = mo_dim1, y = mo_dim2, colour = profile_id)) +
geom_point(show.legend = FALSE, size = 0.5, alpha = 0.05)
Tiling
Let’s now tile morphs within the morphological space.
# Folder containing images
img_dir <- "~/Documents/Data/UVP5/images/"
# Number of features to select
n_feat <- 12
# Generate path to image
o <- o %>% mutate(path_to_img = str_c(img_dir, profile_id, "/", object_id, ".jpg"), .before = object_id)
# Prepare a circle for the plot
circ <- circleFun(c(0, 0), 2, npoints = 500)
# Get variables contributions
#to select vars based on contribution to each plane
contribs <- as.data.frame(mo_space$var$contrib) %>% as.data.frame()
colnames(contribs) <- str_c("mo_dim", paste(c(1:ncol(contribs))))
contribs <- contribs %>%
rownames_to_column(var = "feature") %>%
as_tibble() %>%
mutate(
mo_dim_12 = abs(mo_dim1) + abs(mo_dim2),
mo_dim_23 = abs(mo_dim2) + abs(mo_dim3),
mo_dim_34 = abs(mo_dim3) + abs(mo_dim4)
)
# List variables with higher contribution for plane 1:2
var_contrib_12 <- contribs %>%
arrange(desc(mo_dim_12)) %>%
slice(1:n_feat) %>%
pull(feature)
# and for plane 3:4
var_contrib_34 <- contribs %>%
arrange(desc(mo_dim_34)) %>%
slice(1:n_feat) %>%
pull(feature)
# Get types of features
feat_types <- read_csv("data/raw/features_qual.csv", show_col_types = FALSE)
# Set colour per type of feature, using a named vector
feat_colours <- brewer_colors(length(unique(feat_types$type)), "Set2") # pick the appropriate number of colours
names(feat_colours) <- sort(unique(feat_types$type)) # add names to colours
#homogenize scaling between individuals & variables for correct biplot
# Change scaling of variables/columns from scaling 1 to 2
var_scores <- as.data.frame(t(t(mo_space$var$coord) / sqrt(mo_space$eig[,1]))) # de-scale
var_scores_2 <- as.data.frame(t(t(var_scores) * sqrt(nrow(var_scores) * mo_space$eig[,1]))) # re-scale
# Rename columns
colnames(var_scores_2) <- str_c("mo_dim", paste(c(1:ncol(var_scores_2))))
# Add feature names
var_scores_2 <- var_scores_2 %>%
rownames_to_column(var = "feature") %>%
as_tibble() %>%
# and types
left_join(feat_types, by = join_by(feature))
# Compute length of projection to scale circle
var_scores_2 <- var_scores_2 %>%
mutate(
len_12 = sqrt(mo_dim1^2 + mo_dim2^2),
len_34 = sqrt(mo_dim3^2 + mo_dim4^2),
)Objects in morphospace for axes 1:2
k <- max(var_scores_2$len_12) # adapt scaling of circle to fit the arrows
p12 <- ggmorph_tile(mo_space, o$path_to_img, steps = 10, n_imgs = 3, fun = preprocess, dimensions = c(1,2), scale = 0.02)
p12 +
geom_path(data = circ, aes(x = x*k, y = y*k), lty = 2, color = "grey", alpha = 0.7) +
geom_hline(yintercept = 0, color="grey", alpha = 0.9) +
geom_vline(xintercept = 0, color="grey", alpha = 0.9) +
geom_segment(data = var_scores_2 %>% filter(feature %in% var_contrib_12), aes(x = 0, xend = mo_dim1, y = 0, yend = mo_dim2, colour = type), arrow = arrow(length = unit(0.025, "npc"), type = "open")) +
geom_text_repel(data = var_scores_2 %>% filter(feature %in% var_contrib_12), aes(x = mo_dim1, y = mo_dim2, label = feature, colour = type), show.legend = FALSE) +
scale_colour_manual(values = feat_colours) +
labs(colour = "Feature\ntype")
PC1 = size
PC2 = transparency
Objects in morphospace for axes 2:3
k <- max(var_scores_2$len_34) # adapt scaling of circle to fit the arrows
p34 <- ggmorph_tile(mo_space, o$path_to_img, steps = 10, n_imgs = 3, fun = preprocess, dimensions = c(3,4), scale = 0.02)
p34 +
geom_path(data = circ, aes(x = x*k, y = y*k), lty = 2, color = "grey", alpha = 0.7) +
geom_hline(yintercept = 0, color="grey", alpha = 0.9) +
geom_vline(xintercept = 0, color="grey", alpha = 0.9) +
geom_segment(data = var_scores_2 %>% filter(feature %in% var_contrib_34), aes(x = 0, xend = mo_dim3, y = 0, yend = mo_dim4, colour = type), arrow = arrow(length = unit(0.025, "npc"), type = "open")) +
geom_text_repel(data = var_scores_2 %>% filter(feature %in% var_contrib_34), aes(x = mo_dim3, y = mo_dim4, label = feature, colour = type), show.legend = FALSE) +
scale_colour_manual(values = feat_colours) +
labs(colour = "Feature\ntype")
PC3 = elongation
PC4 = heterogeneity of grey levels
Diversity
Morphospace features
We can collect the position of objects in the morphospace to summarise the morphological diversity of each profile.
# Compute mean and sd of dim1, dim2, dim3 and dim4 per profile
mo_div_prof <- o %>%
group_by(profile_id, lon, lat) %>%
summarise(across(mo_dim1:mo_dim4, list(mean = mean, sd = sd))) %>%
ungroup()
# And store this with profiles data
profiles <- profiles %>% left_join(mo_div_prof, by = join_by(profile_id, lon, lat))And we can plot maps of mean dim1 and dim2 values for each profile.
ggmap(
profiles,
"mo_dim1_mean",
type = "point",
palette = div_pal
) +
labs(colour = "PC1\nSize")
ggmap(
profiles,
"mo_dim2_mean",
type = "point",
palette = div_pal
) +
labs(colour = "PC2\nTransparency")
ggmap(
profiles,
"mo_dim3_mean",
type = "point",
palette = div_pal
) +
labs(colour = "PC3\nElongation")
ggmap(
profiles,
"mo_dim4_mean",
type = "point",
palette = div_pal
) +
labs(colour = "PC4\nGrey hetero.")
We can also look at variance within profiles.
ggmap(
profiles,
"mo_dim1_sd",
type = "point"
) +
labs(colour = "PC1 sd\nSize")
ggmap(
profiles,
"mo_dim2_sd",
type = "point"
) +
labs(colour = "PC2 sd\nTransparency")
ggmap(
profiles,
"mo_dim3_sd",
type = "point"
) +
labs(colour = "PC3 sd\nElongation")
ggmap(
profiles,
"mo_dim4_sd",
type = "point"
) +
labs(colour = "PC4 sd\nGrey hetero.")
Metrics
Multivariate morphological diversity metrics have been defined in Beck et al. 2023 following the definition of multivariate functional diversity metrics in Villeger et al. 2008:
morphological richness
morphological evenness
morphological divergence
Actually there is now a R package to compute these metrics. See Magneville et al. 2021 as well as mFD package. Yay!
Computing these metrics require defining “morphs” (i.e. morphologically similar organisms) in the morphospace, i.e. using kmeans. These morphs are then used instead of species to compute morphological diversity metrics.
Define morphs
Define morphs using kmeans, in parallel.
If we retain n morphospace axes, then we need at least n+1 morphs to be present in each profile (to compute a convex hull in n dimensions, we need n+1 points).
# Number of clusters
n_clust <- 200
# Perform clustering
morphs <- wkmeans::wkmeans(
x = o %>% select(contains("dim")), # use PCA outputs
k = n_clust, # number of clusters
nstart = 50, # number of random initialisations, higher is better
cores = n_cores
)
# Add cluster to table of objects
o <- o %>% mutate(
morph = morphs$cluster,
morph = str_pad(morph, width = nchar(n_clust), pad = "0"), # add leading zeros
morph = paste0("morph_", morph), # Add "morph_" in front
morph = as.factor(morph) # convert to factor
)Look at size of generated morphs (the red vertical line shows the expected mean).
morphs_size <- morphs$size %>%
as.data.frame() %>%
as_tibble() %>%
rename(morph = Var1, n = Freq)
summary(morphs_size) morph n
1 : 1 Min. : 598
2 : 1 1st Qu.:1219
3 : 1 Median :1483
4 : 1 Mean :1605
5 : 1 3rd Qu.:1908
6 : 1 Max. :3660
(Other):194 morphs_size %>%
ggplot() +
geom_histogram(aes(x = n), bins = n_clust/2) +
geom_vline(xintercept = nrow(o)/n_clust, colour = "red")
Relation between morph, taxa and profiles.
Number of individuals of each taxon per morph.
# Counts per morph and per taxa
counts_mo_t <- o %>% select(morph, taxon) %>% count(morph, taxon)
counts_mo_t %>%
ggplot() +
geom_boxplot(aes(x = taxon, y = n)) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
labs(y = "Number per morph") +
scale_y_continuous(trans = "log1p")
Look at number of taxa per morph.
# Counts per morph
counts_mo <- counts_mo_t %>% count(morph)
ggplot(counts_mo) +
geom_histogram(aes(x = n, fill = morph), binwidth = 1, show.legend = FALSE) +
labs(x = "Number of taxa per morph") +
theme_classic()
# Each colour bloc represents a morph
counts_mo %>% summary() morph n
morph_001: 1 Min. : 8.00
morph_002: 1 1st Qu.:15.00
morph_003: 1 Median :18.00
morph_004: 1 Mean :17.93
morph_005: 1 3rd Qu.:21.25
morph_006: 1 Max. :27.00
(Other) :194 The median of number of taxa per morph is 18: morphs are not representative of taxa.
In how many morphs is a taxa present?
# Counts per taxa
counts_t <- counts_mo_t %>% count(taxon)
ggplot(counts_t) +
geom_col(aes(x = taxon, y = n)) +
labs(y = "Number of morphs in which taxon is present") +
coord_flip()
counts_t %>% summary() taxon n
Length:28 Min. : 38.00
Class :character 1st Qu.: 94.25
Mode :character Median :133.50
Mean :128.07
3rd Qu.:167.00
Max. :199.00 Gymnosomata and Cephalopoda are present in less than 50 morphs, while Copepoda are present in all of them.
Number of morphs per profile. This limits the number of dimensions we can use to compute metrics. We need at least n+1 morphs per profile with n the number of dimensions.
count_p_m <- o %>% count(profile_id, morph)
count_p <- count_p_m %>% count(profile_id) %>% arrange(n)
count_p %>%
ggplot() +
geom_histogram(aes(x = n, fill = n >= 6 ), bins = 50) +
geom_vline(xintercept = 6, colour = "red")
The red line shows the minimum number of morphs that must be present in each profile in order to compute morphological diversity metrics using 5 morphospace axes.
Plot clusters
o %>%
ggplot(aes(x = mo_dim1, y = mo_dim2, colour = morph)) +
geom_point(show.legend = FALSE, size = 0.5, alpha = 0.05)
Compute metrics
We need the following matrices:
traits values for each morph centre (morphs × traits)
morphs assemblages (profiles × morphs)
The following metrics are computed (see Magneville et al. 2022):
fric(functional richness): The volume of the convex hull shaping the species present in the assemblagefide(functional identity): The weighted average position of species of the assemblage along each axis. NB: note computed as we already have individuals projections on PCA axes.fdis(functional dispersion): The weighted deviation to center of gravity (i.e. defined by the FIde values) of species in the assemblagefdiv(functional divergence): The deviation of biomass-density to the center of gravity of the vertices shaping the convex hull of the studied assemblagefeve(functional evenness): The regularity of biomass-density distribution along the minimum spanning tree (i.e. the tree linking all species of the assemblage with the lowest cumulative branch length) for the studied assemblagefori(functional originality): The weighted mean distance to the nearest species from the global species poolfspe(functional specialisation): The weighted mean distance to the centroid of the global species pool (i.e. center of the functional space)fmpd(functional mean pairwise distance): The mean weighted distance between all pairs of speciesfnnd(functional mean nearest neighbour distance): The weighted distance to the nearest neighbour within the assemblage
# Matrix of trait values for each morph, i.e. centers of morphs in mspace
# - rows = morphs
# - columns = traits
mo_coord <- as_tibble(morphs$centers) %>%
mutate(
morph = row_number(),
morph = str_pad(morph, width = nchar(n_clust), pad = "0"),
morph = paste0("morph_", morph)
) %>%
column_to_rownames("morph") %>%
as.matrix()
# Matrix summarising morphs assemblages
# - rows = profiles (as row names)
# - columns = morphs
weights <- o %>%
# concentration per date per morph
group_by(profile_id, morph) %>%
summarise(n = n()) %>%
ungroup() %>%
arrange(morph) %>%
# convert to wide format and fill with 0s
pivot_wider(names_from = morph, values_from = n, values_fill = 0) %>%
column_to_rownames("profile_id") %>% # set profile_id as rowname
as.matrix()
# Compute diversity metrics, which takes a looooooooong time
morpho_div <- alpha.fd.multidim(
sp_faxes_coord = mo_coord,
asb_sp_w = weights,
ind_vect = c("fdis", "fmpd", "fnnd", "feve", "fric", "fdiv", "fori", "fspe"),
details_returned = FALSE,
verbose = FALSE
)
# Clean result
morpho_div <- morpho_div$functional_diversity_indices %>%
rownames_to_column(var = "profile_id") %>%
as_tibble() %>%
select(-sp_richn) %>%
# rename metrics from functional to morphological
set_names(~ str_replace_all(., "^f", "mo_"))
# And add to table of profiles
profiles <- profiles %>%
left_join(morpho_div, by = join_by(profile_id))Plot maps of resulting morphological diversity metrics
ggmap(profiles, var = "mo_ric", type = "point")
ggmap(profiles, var = "mo_dis", type = "point")
ggmap(profiles, var = "mo_div", type = "point")
ggmap(profiles, var = "mo_eve", type = "point")
ggmap(profiles, var = "mo_ori", type = "point")
ggmap(profiles, var = "mo_spe", type = "point")
ggmap(profiles, var = "mo_mpd", type = "point")
ggmap(profiles, var = "mo_nnd", type = "point")
Save
Let’s rename morphospace axes according to what we found to make them more meaningful.
profiles <- profiles %>%
rename(
mo_size_mean = mo_dim1_mean, # size (positive values = bigger)
mo_grey_mean = mo_dim2_mean, # grey (positive values = transparent, i.e. higher grey values)
mo_elon_mean = mo_dim3_mean, # elongation (positive values = elongated)
mo_ghet_mean = mo_dim4_mean, # grey heterogeneous (positive values = heterogeneous)
mo_size_sd = mo_dim1_sd,
mo_grey_sd = mo_dim2_sd,
mo_elon_sd = mo_dim3_sd,
mo_ghet_sd = mo_dim4_sd,
)#|cache: false
save(profiles, file = "data/03.uvp_profiles.Rdata")